Not any triple \((\mathbf {a}, \, \mathbf {d}, \, \xi )\)  admits a canonical harmonic field.
Ignat and Jerrard [1]}
characterised the values of \((\mathbf {a}, \, \mathbf {d}, \, \xi )\) 
that admit a canonical harmonic field; we recall their result.
We say that a set \(L\subseteq \mathrm {Harm}^1(M)\) 
is an affine lattice if there exists a linear, invertible
map \(\alpha \colon \mathrm {Harm}^1(M)\rightarrow \mathbb {R}^{2\mathfrak {g}}\)  and a vector \(b\in \mathbb {R}^{2\mathfrak {g}}\) 
such that \(\alpha (L) = \mathbb {Z}^{2\mathfrak {g}} + b\) .
